I honestly am going to try and reply to all of these individually because these are all excellent. This one caught my attention the most so I'll start here:

1. You are right about the amateurs and all that. Our keyboardist is a trained church organist, was the organist at this church for years and plays quite frequently since the current organist at the traditional service is terminally ill. Other than him, none are really professional. All are good though.
2. The monitors are completely out of our control, our soundman controls everything. Truthfully, if she were one of the ones that were there from the beginning and I hadn't seen all the other crap she's done, this wouldn't have bothered me as badly. When you're new though, it's a pretty big stretch. And couldn't she have asked to have herself turned up? Anyway, we're changing our sound setup so that the way the mix sounds in the monitors is the same way that it sounds out front, so this could shut her up.

Ah, organs... the classic "church" instrument, and the cause of so many train wrecks, unless you've got them in monitors. In the one church band I played in with an organ and a trained organist, the worship leader loved to have her start out songs. What I could never get across to him was that, due to the muddy room acoustics and the organ not being in the monitors at all, I could never hear her individual notes well enough to pick out the tempo she was playing.

As far as monitors and soundmen and control, again, this is part and parcel of the worship leader's responsibilities. If he notices that the sound guy can't get it dialed in, it's up to him to fix it, and this means anything and everything from having him trained/retrained, to replacing him. A great long-term investment for your worship team is true personal monitor systems with in-ear sound. I would actually invest in that ahead of new drums or cymbals.

Looks like your dad is getting the message about this one person, but I would advise caution and restraint. Nothing will poison a worship team more than getting a reputation as a political clique. I don't think any worship team should be forced to accept anyone with ego or talent issues, and there should be room for musical growth on the team. But for anyone to have a diva attitude in a worship team is to completely miss the point of worship in the first place. Lots of luck with this!